Effects of Frequency on Resistance in Tuned Circuits
In the expression for inductive reactance, XL = 2 p fL, and in the expression for capacitive reactance,
both contain "f" (frequency). Any effects of frequency changes the reactance of the circuit components as already explained. So far, nothing has been said about the effect of frequency on resistance. In an Ohm's law relationship, such as R = E/I no "f" is involved.
Thus, for all practical purposes, a change of frequency does not affect the resistance of the circuit. If a 60-hertz a.c. voltage causes 20 milliamperes of current in a resistive circuit, then the same voltage at 2000 hertz, for example, would still cause 20 milliamperes to flow.
NOTE: Remember that the total opposition to a.c. is
called impedance (Z). Impedance is the combination of inductive
reactance (XL), capacitive reactance (XC), and resistance (R). When
dealing with a.c. circuits, the impedance is the factor with which you
will ultimately be concerned. But, as you have just been shown, the
resistances (R) are not effects of frequency. Therefore, the remainder
of the discussion of a.c. circuits will only be concerned with the
reactance of inductors and capacitors and will ignore resistance.
A.c. Circuits Containing Both Inductive and Capacitive Reactances
A.c. circuits that contain both an inductor and a capacitor have interesting characteristics because of the opposing effects of L and C. X L and XC may be treated as reactors which are 180 degrees out of phase. As shown in figure 1-2, the vector for XL should be plotted above the baseline; vector for XC, figure 1-3, should be plotted below the baseline. In a series circuit, the effective reactance, or what is termed the RESULTANT REACTANCE, is the difference between the individual reactances. As an equation, the resultant reactance is:
X = XL - XC
Suppose an a.c. circuit contains an XL of 300 ohms and an XC of 250 ohms. The resultant reactance is:
X = XL - XC = 300 - 250 = 50 ohms (inductive)
In some cases, the XC may be larger than the X L. If XL = 1200 ohms and X C = 4000 ohms, the difference is: X = XL - XC = 1200 - 4000 = - 2800 ohms (capacitive). The total carries the sign (+ or - ) of the greater number (factor).